June 19, 2011

Knot Theory gets major newspaper coverage!

On Friday, June 17, Japan’s second most-read newspaper, Asahi Shimbun, ran a full-page story on Knot Theory!!! Because of the sudden media exposure, I’ve been getting e-mails from family in Japan like studying Knot Theory makes me some kind of a celebrity. I’m sure it’s the same for every Knot Theorist who’s lived there- we’re enjoying our 15 minutes of fame right now.
The story is occasioned by the release of a fun computer game based on a theorem of Ayaka Shimizu. Ayaka is a member of Akio Kawauchi’s Knot Theory group at OCAMI. The theorem appears in her preprint Region crossing change is an unknotting operation.

At a seminar in Osaka City University, Kengo Kishimoto suggested the “region crossing change” as an unknotting move. A knot diagram divides a plane up into regions, and a region crossing change is a move which changes all crossings adjacent to a region.
Ayaka was able to show that any knot diagram can be untied using region crossing changes. But she also showed that any knot diagram can be made positive by region crossing changes. This was recently extended by Cheng Zhiyun and Gao Hongzhu to 2-component links with even linking number.
So what do you do with a beautiful result like that? Kawauchi, Shimizu, and Kishimoto turned it into an addictive computer game! I must say, their game is the most fun game I’ve seen come out of topology. Watch out Tetris! This game is fun, and you don’t need to know any topology in order to play it. The goal is to colour all crossings “red” (i.e. positive crossing) by region crossing changes. Play and give it to your cousins and uncles and aunts to play!
To play the game click HERE.
Asahi Shimbun picked up that this was an amazing new gaming idea, and took the opportunity to run a full-page spread on Knot Theory. Their article does an amazing job of selling us, with sentences like “not only is knot theory a fascinating modern area of research, but the power and simplicity of its methods have captured the attention of chemists and biologists the world over.”
I vote this article as one of the best media exposures mathematics has ever had. Congratulations to the OCAMI crew for pulling this off!

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The text is just an explanation of the rules (click regions to change colours of adjacent crossings), and credits.
Also, the newspaper article is in Japanese, and what’s online is just a small excerpt. I should really scan and translate, shouldn’t I…
Click on the pictures to play for that knot diagram!

I love the idea of turning a proof into a fun game!
They’re a group of topologists, so I don’t know whether they’ll be able to make a professional-looking gaming interface, but with the press coverage this has been getting, I dream that a game design company might become interested, and then professionals would design a lovely interface, use many more knots, maybe put a timer and music in… Imagine seeing some teenager playing that game on their cellphone on the subway!

Recently, it was proved that region crossing change is an unknotting operaiton on a link diagram if and only if the link is a proper link, i.e. every individual component has even total linking number with the other components. But I have not submitted this paper to arXiv yet.
In fact in my opinion, the behavior of region crossing changes is also well understood, i.e. crossing points that can be switched by region crossing changes satisfy some condition, and this condition is also sufficient.

Good for OCAMI, in China I hardly read this kind of mathematic news on newspaper…